In this study, we investigate the form of the solutions of the following rational difference equation systems? , , such that their solutions are associated with Padovan numbers.
<span style="white-space:normal;">This paper studies the influence factors of atoms number (N) at temperature (T) and after annealing time (t) on the structure shape and the plastic deformation of Poly...<span style="white-space:normal;">This paper studies the influence factors of atoms number (N) at temperature (T) and after annealing time (t) on the structure shape and the plastic deformation of Polyethylene C</span><sub style="white-space:normal;">2</sub><span style="white-space:normal;">H</span><sub style="white-space:normal;">4</sub><span style="white-space:normal;"> (PE) by the Molecular Dynamics (MD) method with Dreading pair interaction, cyclic boundary conditions and plastic deformation of Polyethylene (PE) be done by stretching method according to the z-axis. The results of structure, plastic deformation of PE are analyzed through size (l), the total energy of the system (E</span><sub style="white-space:normal;">tot</sub><span style="white-space:normal;">), shape and associated energy (E</span><sub style="white-space:normal;">bond</sub><span style="white-space:normal;">), angular binding energy (E</span><sub style="white-space:normal;">angle</sub><span style="white-space:normal;">), energy E</span><sub style="white-space:normal;">dihedral</sub><span style="white-space:normal;">, interactive energy Vander Walls (E</span><sub style="white-space:normal;">non-bonding</sub><span style="white-space:normal;">). When increasing N, t leads to the number of structural units of Face-Centred Cubic (FCC), Body-Centered Cubic (BCC) and Hexagonal Close-Packed (HCP) increasing, but Amorphous (Amor) decreases while the angle between the atoms is a constant corresponding to 109.5</span>°<span style="white-space:normal;">. Besides, the length of the link (r) increases from r = 1.529 </span>Å<span style="white-space:normal;"> to r = 1.558 </span>Å<span style="white-space:normal;"> while the plastic deformation energy of PE gets an enormous change and the bonding angle at 109.27</span>°<span style="white-space:normal;">. The length of the link r = 1.529 </span>Å<span style="white-space:normal;"> and the size (l) of the PE material increase from l = 3.73 nm to l = 6.63 nm while the total energy of system (E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;">) decreases from E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>1586 eV to E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>7891 eV with the transition temperature is T = 103 K. Increasing the number of atoms leads to increasing the length of the link. The total energy E</span><sub style="white-space:normal;">total </sub><span style="white-space:normal;">of the system decreases, but the number of structural units in FCC, HCP, BCC and Amor increase, which leads to the length of the link increases, the E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> decreases, and there is a change in the plastic deformation characteristics of PE. In contrast, increasing T leads to the plastic deformation increases, and PE moves from the amorphous state to the liquid state. The obtained results are very significant for future experimental research.</span>展开更多
基金supported by National Natural Science Foundation of China,China(No.52101138)Natural Science Foundation of Hubei Province,China(No.2020CFB259)+7 种基金Shenzhen Science and Technology Program,China(No.JCYJ20220530160813032)State Key Lab of Advanced Metals and Materials,China(No.2020-Z01)State Key Laboratory for Mechanical Behavior of Materials,China(No.20202205)Guangdong Basic and Applied Basic Research Foundation,China(Nos.2020A1515110531,2021A1515111122)State Key Laboratory of Materials Processing and Die&Mold Technology,Huazhong University of Science and Technology,China(No.P2021-021)support from the National Natural Science Foundation of China(No.12004294)National Youth Talents Programsupport by Center for Alloy Innovation and Design(CAID)and HPC platform of Xi’an Jiaotong University。
文摘In this study, we investigate the form of the solutions of the following rational difference equation systems? , , such that their solutions are associated with Padovan numbers.
文摘<span style="white-space:normal;">This paper studies the influence factors of atoms number (N) at temperature (T) and after annealing time (t) on the structure shape and the plastic deformation of Polyethylene C</span><sub style="white-space:normal;">2</sub><span style="white-space:normal;">H</span><sub style="white-space:normal;">4</sub><span style="white-space:normal;"> (PE) by the Molecular Dynamics (MD) method with Dreading pair interaction, cyclic boundary conditions and plastic deformation of Polyethylene (PE) be done by stretching method according to the z-axis. The results of structure, plastic deformation of PE are analyzed through size (l), the total energy of the system (E</span><sub style="white-space:normal;">tot</sub><span style="white-space:normal;">), shape and associated energy (E</span><sub style="white-space:normal;">bond</sub><span style="white-space:normal;">), angular binding energy (E</span><sub style="white-space:normal;">angle</sub><span style="white-space:normal;">), energy E</span><sub style="white-space:normal;">dihedral</sub><span style="white-space:normal;">, interactive energy Vander Walls (E</span><sub style="white-space:normal;">non-bonding</sub><span style="white-space:normal;">). When increasing N, t leads to the number of structural units of Face-Centred Cubic (FCC), Body-Centered Cubic (BCC) and Hexagonal Close-Packed (HCP) increasing, but Amorphous (Amor) decreases while the angle between the atoms is a constant corresponding to 109.5</span>°<span style="white-space:normal;">. Besides, the length of the link (r) increases from r = 1.529 </span>Å<span style="white-space:normal;"> to r = 1.558 </span>Å<span style="white-space:normal;"> while the plastic deformation energy of PE gets an enormous change and the bonding angle at 109.27</span>°<span style="white-space:normal;">. The length of the link r = 1.529 </span>Å<span style="white-space:normal;"> and the size (l) of the PE material increase from l = 3.73 nm to l = 6.63 nm while the total energy of system (E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;">) decreases from E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>1586 eV to E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> = <span style="white-space:nowrap;">−</span>7891 eV with the transition temperature is T = 103 K. Increasing the number of atoms leads to increasing the length of the link. The total energy E</span><sub style="white-space:normal;">total </sub><span style="white-space:normal;">of the system decreases, but the number of structural units in FCC, HCP, BCC and Amor increase, which leads to the length of the link increases, the E</span><sub style="white-space:normal;">total</sub><span style="white-space:normal;"> decreases, and there is a change in the plastic deformation characteristics of PE. In contrast, increasing T leads to the plastic deformation increases, and PE moves from the amorphous state to the liquid state. The obtained results are very significant for future experimental research.</span>